Abstract
We have studied the simultaneous bootstrap of the Rho and f0
mesons, using the Balázs method. When we include the exchange of an
f0 with physical parameters in the input force, we find that we
obtain an approximately self-consistent Rho with a mass of 710 MeV and full
width of 100 MeV; the degree of self-consistency is somewhat improved if
the width is reduced to 66 MeV. One can obtain a simultaneous bootstrap of
both the Rho and f0 with a Rho mass and full width of 710 and 46
MeV, and f0 mass and full width of 1344 and 112 MeV,
respectively. We believe that the double-bootstrap results are somewhat
affected by our approximate treatment of inelastic effects, which involves
a discontinuity in the inelasticity function
RlI near the position of the f0.
These results are based upon taking n, the number of poles
approximating the left-hand cut, equal to 7. The use of a large number of
poles is important, and it is not at all clear from the n dependence
of our calculations that we have yet obtained a limiting form of the
results as n becomes large, even with n=7.
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